Rules
What happens when you need to divide or multiply by a negative?
You flip the sign.
Solve:
45<x-20<67
65<x<87
Solve:
│h+27│> 18
h>-9 or h<-45
Solve:
x+19<42 or x-37≥46
x<13 or x≥83
What does this sign mean?:
<
less than
When graphing, how do you know whether to graph with an open or closed circle?
Closed circle means it could be equal to the number, open means it can't be that number.
Solve:
1-4x<21 and 5x +2≥22
x>-5 and x≥4
Solve:
7│h-14│<42
h<20 and h>8
Solve:
5x÷2<10 or 3x-42≥6
x<4 or x≥16
What does absolute value mean?
The numbers' distance from zero.
Why can an absolute value equation result in no solution if it looked like this?:
│h-27│< -17
An absolute value can't be negative so it can't be less than a negative number.
Solve:
32<2x+84<92
-26<x<4
Solve:
8│h-78│+13<61
h<84 and h>72
Solve:
2x+17> 13 or -3x-2>10
x>-2 or x<-4
What type of inequality is the "and" and the "or?"
Compound inequalities.
What does an "and" inequality look like when graphed?
It is graphed as a range of numbers that can be the answer.
Solve:
2<4x-30≤50
8<x≤20
Solve:
1/2│7x-12│-36≥-28
x≥4 or x≤-4/7
Solve:
x+19<57 or x+24-5>57
x<38 or x>38
What does isolating the variable mean?
Getting the variable by itself to one side.
How can you tell if an absolute value inequality is an "and" inequality or an "or" inequality?
The < and ≤ means it's an "and" inequality. The > and ≥ means its an "or" inequality.
Solve:
57<7x-24+13≤108
68/7<x≤17
Solve:
│2h-37│+85<36
h>43 and h<-6
Solve:
-2x + 37 -18<43 or 3x-12>22
x>34/3
("or" inequality only needs to satisfy one inequality)
What is the difference between "and" inequalities and "or" inequalities?
"And" inequalities show a range of numbers that can work or be a possible solution to that inequality. An "or" inequality specifically shows the numbers that can not be an answer to that inequality. It is graphed as going in opposite directions but avoiding one area completely. So while still giving a range of numbers that could possibly be the answer it shows that certain numbers cannot be the solution.